Computer Vision and Image Understanding
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Stabilizing Image Mosaicing by Model Selection
SMILE '00 Revised Papers from Second European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Triangulation for points on lines
Image and Vision Computing
Error Analysis in Homography Estimation by First Order Approximation Tools: A General Technique
Journal of Mathematical Imaging and Vision
Optimal two-view planar scene triangulation
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
Triangulation for points on lines
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
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We address the problem of finding optimal point correspondences between images related by a homography: given a homography and a pair of matching points, determine a pair of points that are exactly consistent with the homography and that minimize the geometric distance to the given points. This problem is tightly linked to the triangulation problem, i.e., the optimal 3D reconstruction of points from image pairs. Our problem is non-linear and iterative optimization methods may fall into local minima. In this paper, we show how the problem can be reduced to the solution of a polynomial of degree eight in a single variable, which can be computed numerically. Local minima are thus explicitly modeled and can be avoided. An application where this method significantly improves reconstruction accuracy is discussed. Besides the general case of homographies, we also examine the case of affine transformations, and closely study the relationships between the geometric error and the commonly used Sampson's error, its first order approximation. Experimental results comparing the geometric error with its approximation by Sampson's error are presented.